The measure of the angle is 36.9^o. Option B.
What is a right triangle?A right triangle is a form or type of triangle in which the measure of one of its internal angles is 90^o. As such, either the trigonometric functions or Pythagorean theorem can be applied to determine any of its properties as the case may be.
From the details given in the question, we can deduced that;
Sin θ = 3/5
= 0.6
So that,
θ = Sin^-1 0.6
= 36.87
θ = 36.9^o
The measure of the angle is 36.9^o. Option B.
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Solve for x. Round to the nearest tenth, if necessary.
x=15.4 units
Step-by-step explanation:First, some definitions before working the problem:
The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.
The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.
Working the problem
For the given triangle, the right angle is at the bottom, so the side on top is the hypotenuse. We know the angle in the upper right corner, so the side across from it with length 4.5, is the opposite side.
For this triangle, the "opposite" leg is known. Additionally, the "hypotenuse" is unknown and is our "goal to find" side.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh". So, the desired function to use for this triangle is the Sine function.
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]sin(17^o)=\dfrac{4.5}{x}[/tex]
Multiply both sides by x, and divide both sides by sin(17°)...
[tex]x=\dfrac{4.5}{sin(17^o)}[/tex]
Make sure your calculator is set to degree mode, and calculate:
[tex]x=\dfrac{4.5}{0.2923717047227...}[/tex]
[tex]x=15.391366289249...[/tex] units
Rounded to the nearest tenth...
[tex]x=15.4[/tex] units
Find the shortest path from vertex A to vertex L. Give your answer as a sequence of vertexes, like ABCFIL
The shortest path from vertex A to vertex L is ACFIL. The total distance of the path is 27 units.
To find the shortest path from vertex A to vertex L, we can use Dijkstra's algorithm. We start by marking the distance of each vertex from A as infinite except for A, which is 0. Then, we choose the vertex with the smallest marked distance and update the distances of its neighbors. We repeat this process until we reach L.
In this case, we would start at A and update the distances of B and D to 2 and 19, respectively. We would then choose B and update the distances of C, F, and E to 11, 10, and 18, respectively.
Next, we would choose F and update the distances of I and L to 27 and 30, respectively. Finally, we would choose L and have found the shortest path from A to L: ACFIL with a total distance of 27.
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In urgent need of assistance pls and thanks
The addition of the vectors [tex]\vec a + \vec b[/tex] is (3, -5) and it has been represented by using the head to tail method in the graph below.
What is a vector?In Mathematics and Science, a vector can be defined as an element of a vector space, which represents an object that is composed of both magnitude and direction.
How to add vectors by using the head to tail method?In Mathematics and Science, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Generally speaking, the head to tail method of adding two (2) vectors involve drawing the first vector ([tex]\vec a[/tex]) on a cartesian coordinate and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Lastly, the resultant vector is then drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By solving the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)
[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))
[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]
[tex]\vec a + \vec b[/tex] = (3, -5).
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The cost of 8 T-shirts and 3 jackets is $135. The cost of 7 T-shirts and 5 jackets is $149.
Enter the cost of one T-shirt and one jacket in the response boxes below.
T-shirt: S
jacket: $
The cost of one T-shirt and one jacket is $12 and $13 respectively.
What is the cost of one T-shirt and one jacket?Let
cost of one t-shirt = x
cost of one jacket = y
8x + 3y = 135
7x + 5y = 149
Multiply (1) by 5 and (2) by 3
40x + 15y = 675
21x + 15y = 447
Subtract the equations to eliminate y
40x - 21x = 675 - 447
19x = 228
divide both sides by 19
x = 228/19
x = 12
Substitute x = 12 into (1)
8x + 3y = 135
8(12) + 3y = 135
96 + 3y = 135
3y = 135 - 96
3y = 39
y = 39/3
y = 13
Hence, a T-shirt and a Jacket cost $12 and $13 respectively.
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Jeff is buying tickets for a group of concerts. He wants tickets for at least 8 concerts. Each ticket for an afternoon concert costs $15 and each ticket for an evening concert costs $30. Jeff wants to spend no more than $300.
Which system of inequalities can Jeff use to find the number of tickets he can buy?
A. x + y ≥ 8 and 300 ≥ 15x + 30y
B. x + y ≤ 8 and 300 ≥ 15x + 30y
C. x + y ≥ 300 and 8 ≥ 15x + 30y
D. x + y ≤ 300 and 8 ≤ 15x + 30y
Answer:
(A.)
Step-by-step explanation:
you just have to follow the order that there going in so when they say less than you use the less than sign
